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Scale Rules

Length Measures

Although shared words for units of measurement—typically body parts such as "hand" and "foot"—dated back to ancient times, the lengths of these units differed by local custom. By the 17th and 18th centuries, each European city had its own standard for length measures. Many places called this standard an "ell," although the spelling of the word varied. When this Museum opened in 1964, the curators collected original objects and reproductions to show how the mathematics of European daily life had been transported into American business and trade. One particular treasure is a pedometer made by Jacob Ramminger in Stuttgart, Germany, around 1600.

As national states unified formerly decentralized localities and as trade between different areas of Europe increased, governments made efforts to define national standards. The English lengths for the inch, foot, and yard were perhaps most prominent around the world, and they were utilized in the American colonies. In both the Articles of Confederation and the U.S. Constitution, the federal government reserved for itself the power to fix national weights and measures. Shortly thereafter, in the 1790s, scientists working for the French government developed the metric system, in which one meter represented one ten-millionth of the distance between the North Pole and the Equator. Although copies of metric standards were brought to the United States, Americans maintained a complicated relationship with the system of measurement. For instance, John Quincy Adams investigated the system in 1821; Charles Davies evaluated it again in 1867. Both men recommended that adoption of metric measurements be delayed since English units were so well established in American commerce.

In addition to examples of yard and meter standards from the 19th and 20th centuries and other efforts to promote the metric system, the collection has one of the rules Scottish Astronomer Royal Charles Piazzi Smyth distributed in an unsuccessful effort to prove that the system of measurement used by ancient Egyptians to build the pyramids correlated with the modern English system. There are also several rulers brought by the nation of Japan to the 1876 World's Fair to demonstrate its ability to adopt European units. Finally, this page contains some rules made by the notable American manufacturers Stanley and Lufkin and some rulers used in schools.

Laurits Christian Eichner (1894–1967) was a Danish engineer who married an American, Sarah Craven, and settled in Bloomfield, N.J., in 1925. During the Depression, he began marketing his skills as a metal craftsman, eventually branching out from bronze bowls and pewter tableware to replicas of historical scientific instruments and modern precision instruments, such as interferometers, astrophotometers, and telescopes. In the 1950s the Smithsonian hired him to restore and reproduce instruments and machines in preparation for the opening of the Museum of History and Technology (now the National Museum of American History).

Eichner's workshop made this octagonal wooden rule from an original at the Adler Planetarium in Chicago. The larger end is marked: LCE (/) 1964. An ivory handle around the larger end has black geometric markings. Ivory plates on each side of the rule show the length of the ell, a traditional "arm's length" measurement, in eight German cities. (One plate is broken.) Each side also has rounded notches marking off divisions for each length of ell.

This small brass rule has two linear scales, one labeled "4" that is divided to quarter-units and numbered by ones from 30 to zero, and one labeled "3" that is divided to quarter-units and numbered by ones from 22 to zero. The units are 0.5 cm (7/32") and 0.7 cm (9/32") long, respectively. A brass peg is in the center of the rule, and a small round hole is on the right edge. These suggest the rule was designed to attach to other rules, although no such rules were received with the instrument.

While the scales are in a 4:3 proportion to each other, the pre-metric units of measurement represented by either scale are not known. The length of the divided portion (15.6 cm or 6-3/16") is almost exactly half the length of the average fuss (31.4 cm or 12.36"), a traditional "foot" measure used in German-speaking areas of Central Europe.

The top edge of the rule is marked: Antonius Braun Invenit et Fecit 1722. Anton Braun (1685–1728), a native of Swabia in southwest Germany, made instruments in Prague by 1720 and in Vienna by 1724. In 1727 he built a pinwheel calculator during a competition to become chief instrument maker for Holy Roman Emperor Karl VI.

This European triangular wooden length measure is crudely carved on all three sides with letters, suns, a girl, fish, and geometric figures. One side reads: MD 1727. Another side reads: P q R S T V W X | Z. Each side has seven wooden pegs, roughly evenly spaced at approximately 7.5 cm. The side with the partial alphabet has two additional pegs (one missing) at the ends of the rule. The Smithsonian acquired this object in 1960.

This octagonal wooden rule has a handle and a measuring part that is broken off at the end. Both parts are crudely but prolifically carved with Xs, triangles, curves, and diamonds. One face is carved with a number: 1756. Another face is notched with measuring marks. These are placed 4, 6.3, 10.8, 19.4, 26, and 53.5 cm from the base of the handle. Compare to MA*318246, MA*318247, and MA*318248.

This square, tapering wooden rule has a brass tip around the narrow end. Three sides are finely carved with fruit and vines, possibly oranges and pineapples. The fourth side is marked with inlaid brass dots: ANNO IIV DB 1757 NAVW. Inlaid brass bars provide measuring marks that are 1, 3.8, 6, 10.2, 18.7, 26, and 53 cm from the wide end. The spacing of the marks is similar to those on MA*318246. The overall length of the rule is 70 cm (27-1/2"), which is close to the usual length for a Flemish ell (68.6 cm, 27").

This European brass rule consists of twelve segments, ten that are 10.5 cm (4-1/4") long and two that are 9.6 cm (3-3/4") long. The segments are riveted together end to end to form a rule about 104 cm (41") long. On one side the rule has scales for Paris and London inches, numbered by ones from 1 to 36. The other side has scales for Venice and Vienna inches, numbered by ones from 1 to 36. On each of the four scales, the first inch is divided to 1/12" and the rest are divided to 1/2".

According to the rule, the Paris inch was 1-3/32" long, the London inch was 1", the Venice inch was 1-1/8", and the Vienna inch was 1-1/32". These lengths are within range of the pre-metric system national standards reported by contemporary arithmetic textbooks and modern historians.

This wooden rectangular rule consists of a carved handle resembling a finial and a tapered, ruled part. The handle is made from a separate piece of wood and attached to the ruled part with a peg. There is an inlaid piece of mother of pearl (1.6 cm X 1.5 cm) on one side. The ruled part is about 71.5 cm long, slightly longer than the average Dutch el (68–70 cm), a traditional "arm's-length" measure.

The rule is marked with grooves (each approximately 1 mm wide) on 2 sides. On the side with the museum mark, the grooves are 3.7, 5.3, 10.3, 20.9, 38.2, and 55.3 cm from the base of the handle (or 68.8, 66.2, 61.2, 50.6, 33.3, and 16.2 cm from the tip). On the side with the mother of pearl piece, the grooves are 27.5, 32.4, 52.5, and 62.6 cm from the base of the handle (or 44.0, 3.1, 19.0, and 9.0 cm from the tip). The mother of pearl inlay is 22.3 cm from the base of the handle (49.2 cm from the tip). Compare to MA*318247, MA*318248, and MA*325404.

Reference: Russ Rowlett, How Many? A Dictionary of Units of Measurement, July 11, 2005, http://www.unc.edu/~rowlett/units/index.html.

This wooden rectangular rule consists of a fluted handle with a carved head at the end and a tapered, ruled part. The rule is cracked between two nails below the handle on the side with the head's face. On the side with the back of the head, the rule is marked with straight lines that are 27.5, 38.5, 42.0, 49.7, 53.2, 56.9, 60.8, 64.5, and 68.1 cm from the base of the handle (or, 44.5, 33.5, 30.0, 22.3, 18.8, 15.1, 11.2, 7.5, and 3.9 cm from the tip of the rule). The mark at 49.7 cm is an asterisk rather than a plain line.

The Dutch el is a traditional "arm's length" measure commonly used before The Netherlands adopted the metric system in 1820. The el was 68–70 cm on average, but this example is slightly longer at 72 cm, excluding the handle. Compare to MA*318246, MA*318248, and MA*325404.

This layered, curved wooden rule has a twisted handle with an ivory crown at the end. A piece of whalebone (2.4 X 1.5 cm) is carved with two horizontal lines and an "X" and is fastened to the rule just below the handle. The measuring part of the rule is 52 cm (20-1/2") long, considerably shorter than the average Dutch el (68–72 cm), a traditional "arm's length" measure used before The Netherlands adopted the metric system in 1820. Also unlike Dutch els such as MA*318246, MA*318247, and MA*325404, there are no grooves marking off distances. Instead, horizontal rows of three nails are placed 5, 9.2, 17.8, and 35 cm from the base of the handle. A diagonal row of four nails is adjacent to the last horizontal row. One layer of wood has been removed from the tip of the rule.

This round wooden yardstick is divided into 16 scales numbered from right to left that divide the foot into various numbers of parts. The scales include: 8 (units of 1 1/2" or 3.8 cm), 9 (1 5/16" or 3.3 cm), 10 (1 3/16" or 3.0 cm), 11 (1 1/16" or 2.7 cm), 12 (1" or 2.6 cm), 13 (11/12" or 2.3 cm), 14 (7/8" or 2.1 cm), 15 (13/16' or 2.0 cm), 16 (3/4" or 1.9 cm), 17 (11/16" or 1.7 cm), 18 (21/32' or 1.6 cm), 19 (5/8" or 1.6 cm), 20 (5/8' or 1.5 cm), 21 (9/16" or 1.5 cm), 22 (17/32" or 1.4 cm), and 23 (1/2" or 1.3 cm) parts per foot. The number of subdivisions per foot is indicated at the right end of each scale, but these marks are badly worn.

The left end of the rule is marked: PSP (/) April 25th (/) 1822. The right end is marked: PSP (/) 1822.

The National Museum of History and Technology, now the National Museum of American History, acquired this calculating stick, probably between 1962 and 1965, for its Growth of the United States exhibition, which opened in 1967 and closed in 1982. See also 1987.0107.05.

Reference: William S. Walker, "A Living Exhibition: The Smithsonian, Folklife, and the Making of the Modern Museum" (Ph.D. diss., Brandeis University, 2007).